The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $ϕ$ linked with the primary coil is given by $ϕ = ϕ_{0} + 4 t$ , where $ϕ$ is in weber, t is time in second and $ϕ_{0}$ is a constant, the output voltage across the secondary coil is :

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90 V

120 V

220 V

30 V

answer is B.

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Detailed Solution

Induced emf in primary coil $E_{p} = \frac{dϕ}{dt} = \frac{d}{dt} (ϕ_{0} + 4 t) = 4 V$

Induced emf in secondary coil

$\frac{E_{s}}{E_{p}} = \frac{N_{s}}{N_{p}} \Rightarrow \frac{E_{s}}{4} = \frac{1500}{50} \Rightarrow E_{s} = 120 V$

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